Summary: A Fractal Representation for Real Optimization
Daniel Ashlock
Department of Mathematics and Statistics
University of Guelph
Guelph, Ontario, Canada, N1G 2W1
dashlock@uoguelph.ca
Justin Schonfeld
Department of Computer Science and Engineering
University of Nevada at Reno
Reno, NV, 89557, USA
shonfju@cse.unr.edu
Abstract-- The chaos game, in which a moving point is
repeatedly averaged toward randomly selected vertices of a
triangle, is one method of generating the fractal called the
Sierpinski triangle. The sequence of vertices, called generators,
used to reach a given point of the Sierpinski triangle yields a
map from strings over a three-character alphabet to points in
the plane. This study generalizes that representation to give a
character-string representation for points in Rn
. This is a novel